Abstract
We present a deep adaptive sampling method for solving PDEs where deep neural networks are utilized to approximate the solutions. More precisely, we propose the failure-informed adaptive sampling for PINNs and an adaptive importance sampling scheme for deep Ritz. Both approaches can adaptively refine the training set with the goal of reducing the failure probability. Applications to both forward and inverse PDEs problems will be presented.
Brief Biography
Zhou Tao is currently a professor at the Chinese Academy of Sciences. His main research areas include uncertainty quantification, numerical PDEs, and parallel-in-time algorithms. He has published over 80 papers in international journals and was invited to write review articles for SIAM Review and Acta Numerica. He received the 3rd Wang Xuan Outstanding Young Scholar Award in 2022. Currently he serves as associate editors for many international journals including SIAM J Numer Anal, SIAM J Sci Comput., and J Sci Comput. He also serves as Vice President of the East Asian Society for Industrial and Applied Mathematics and Editor in Chief of the Society's journal EAJAM.
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